||last updated: 2005-01-18
Given a set of n+1 control points Pi the Bézier curve is
written in terms of Bernstein polynomials:
The curve has the following properties:
- there is no line that has more intersections with a Bézier curve than
with the curve composed by the line segments through the points.
- the curve can be translated and rotated by performing these operations on
the control points.
- a numerical instability for large numbers of control points.
- moving a single control point changes the global shape of the curve.
This can be avoided by smoothly patching together low-order Bézier curves.
The rational Bézier curve is a generalization of the curve:
Another generalization of the curve is the B-spline.